Renyi’s-Tsallis fuzzy divergence measure and its applications to pattern recognition and fault detection

Article type: Research Article

Authors: Kadian, Ratika^{; *} | Kumar, Satish

Affiliations: Department of Mathematics, Maharishi Markandeshwar (Deemed To Be University), Mullana-Ambala, India

Correspondence: [*] Corresponding author. Ratika Kadian. E-mail: kadian.ratika@mmumullana.org.

Abstract: In this communication, we have characterized the sum of two general measures associated with two distributions with discrete random variables as well as fuzzy sets. One of these measures is logarithmic, while other contains the power of variables, named as joint representation of Renyi’s-Tsallis divergence measure which implies that the proposed measure is equal to the constant time the sum of Renyi’s and Tsallis divergence measure. Besides the validation of the proposed measures, some of its major properties are also discussed for probability distributions and fuzzy sets. The performance of the proposed measure is contrasted with other existing measures in the literature. Some illustrative examples are solved in the context of pattern recognition and fault detection problem which demonstrate the practicality and adequacy of measure between fuzzy sets.

Keywords: Renyi’s-Tsallis divergence measure, convex function, fuzzy set, fuzzy divergence measure, pattern recognition, fault detection

Keywords: 94A15, 94A24, 26D15

DOI: 10.3233/JIFS-191689

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 1, pp. 731-752, 2020